Automatic control system



Dec. 29, 1964 R. oLDl-:NBuRGr-:R

AUTOMATIC CONTROL SYSTEM ll Sheets-Sheet 1 Filed Oct. 8, 1953 Dec. 29, 1964 R. OLDENBURGER AUTOMATIC CONTROL SYSTEM Filed oct. 8, 195s ll Sheets-Sheet 2 f f. ---i m -----i---w L@ om m dmazoo N zvzoz m. L 0.. @Q -lliflil-- TMI' malo-rok, '4 QUUJ' O/ce'nbogger J @Mm/m Dec. 29, 1964 Filed Oct. 8, 1953 SERVO SPEE D R. OLDENBURGER AUTOMATIC CONTROL SYSTEM ll Sheets-Sheet 3 Z /N PUT Val-TS CHARACTERISTIC 0F ABSQUARING RESISTORS 148, 380

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AUTOMATIC CONTROL SYSTEM Filed Oct. 8, 1955 ll Sheets-Sheet 5 FROM TACHQHIITER F R001 TACHGHETER ngi- INVENTOR. 'Z' '4' RuFus OLnENuReER Dec. 29, 1964 R. OLDENBURGER AUTOMATIC CONTROL SYSTEM 1l Sheets-Sheet 6 Filed Oct. 8. 1953 I IN VEN TOR RuFus OLDENSUROER M ma Dec. 29, 1964 R. QLDENBURGER 3,163,813

AUTOMATIC CONTROL SYSTEM 11 Sheets-Sheet '7 Filed Oct. 8, 1953 ola 3 NET ourrur 1" .SIGNAL INPUT V01. TS

JNVENTOR. Ru-us OLvENsuRGER Dec. 29, 1964 R. QLDENBURGER 'AUTOMATIC CONTROL SYSTEM 11 Sheets-Sheet 8 Filed OCC. 8, 1953 FSJ Dec. 29, 1964 R. QLDENBURGER AUTOMATIC coNTRor. SYSTEM 11 Sheets-Sheet 9 Filed Oct. 8, 1953 Dec. 29, 1964 R. oLDENBuRGr-:R

AUTOMATIC coNTRQL SYSTEM 1l Sheets-Sheet 10 Filed Oct. 8, 1955 p M/md o l s .w WM v. BM

Dec. 29, 1964 R. OLDENBURGER AUTOMATIC CONTROL SYSTEM 1l Sheets-Sheet 11 Filed Oct. 8, 1953 INVENTOR. RuFus OLDENBURGER United States Patent Otiice alessia Patented Dec. 29, 1964 Illinois lFiled Get. 8, 1953, Ser. No. 384,957 38 Claims. (Cl. S18-448) Inder to Patent Specijication Column Electronic Nonlinear Governor 4 10 Procedure for Adjusting Electronic Nonlinear Governor 8 Preliminary Adjustment for Linear Control 9 Adjustment of Nonlinear Channel Use of Gain Changers Electronic Governor-Se nd E me Electronic Governor-Third Embodiment. Electronic Governor-Fourth Embodiment Electronic Governor-Fifth Embod'nnent.. 20 vElectromagnetic Nonlinear Governor 21 Magnetic Amplifier Circuit 23 Procedure for Adjusting Electromagnetic Governor 24 Use of Gain Changers in Electromagnetic Governor 26 Procedure for Adjusting the Electromagnetic Governor Having Integral Gain Changers 27 Setting the Circuit Constants in the Deviation Channel 29 Setting the Circuit Constants in First Derivative Channel 30 Setting the Circuit Constants in Second Derivative Channel... 30 Limiter Used in Electromagnetic Governor 3l Mechanical Nonlinear Governor 32 Multiplying Device 34 Adjustment of Mechanical Nonlinear Governor 35 The present invention relates to automatic control systems and more particularly to improved means for controlling a variable condition, notably the speed of prime movers and other rotating devices.

While the present devices are particularly suited for the governing of speed, and While the various embodiments ot the invention have been described with emphasis upon speed control, it will be understood that the invention is noty limited thereto and a number or" the concepts and features which are disclosed are applicable in the controlling of other variables such as position, temperature and pressure, to name but a few. For this reason terminology has been used which is applicable to automatic control systems in general and which corresponds to that set forth in Automatic Control Terminology, Paper 52-SA-29 published by the American Society of Mechanical Engineers in 1952.

By definition, an automatic controller isa device which measures the value of a variable quantity or condition and Which operates to restore the condition to a desired reference value. Thus, where it is desired to control the speed of a prime mover in spite of changes in loading, means are provided, in the form of a tachoineter or the like, for measuring the speed. The speed measurement is fed into a controlling means, the output of which iS applied to a motor operator having a rialco'ntrol element. The latter correctively moves a throttle so that the desired speed is restored. Various factors tend to complicate this simple problem and much Work has been done over the years to improve the transient response, in other words to restore the condition to its desired value as quickly as possible and with a minimum of overswing or cycling n about the desired control point.

The present devicek constitutes a departure in speed governing techniques in a number of respects which will become apparent as the discussion proceeds. The invention resides in a new combination of elements which cooperate to produce more precise control with greater rapidity of response than was possible using prior art arrangements. One of the elements in the combination is an absquarer which, in accordance'with the present invention, acts upon a signal representative of the rate of change of the controlled variable, i.e., speed, to. produce at its output an absquare component which is combined with deviation and rate components to drive a servo device which, in turn, correctively adjusts the speed. The absquare concept is novel, having no counterpart in the governor field, and it was necessary to coin a term to describe it.

As used in the present application, the absquare of the first derivative of the deviation is the product of the first derivative multiplied by its absolute value. In order to obtain the absquare signal I prefer to use non-linear resistive materials having a parabolic characteristic and of the type well known in the art as thyrite It will, however, be understood that such material only approximately follows the absquare characteristic defined above. Consequently, when the term absquare is used, it shall be understood to include close practical approximations of the absquare. Furthermore, it is desirable under some circumstances to feed into the absquaring device not only a iirst derivative signal, but also derivative signals of higher order.

Use of the absquare signal is distinguished by full speed of the motor operator for all but small disturbances. The effect is to produce more rapid speed correction than is possible using conventional techniques, since the rate of correction is limited almost entirely by the power capability of the output motor operator or servo device. By Wray of example, it may be assumed that the speed-controlled device, such as a prime mover, suffers a change in speed as a result of a sudden imposition or dropping of the load. Using the present arrangement, the throttle adjusting motor will rotate at full speed in the corrective direction followed by a switch to full speed in the opposite direction to reestablish equilibrium with extreme promptness and without overswing. Using the present arrangement there may, in fact, be more than one such switch point depending upon the number of lags in the system.

For many speed control applications, it is sufhcient to provide means for deriving the absquare of the iirst derivative only. My invention is not, however, limited to this but includes means for deriving the absquare of the sum of the iirst derivative and second derivative functions.

In accordance with one of the aspects of the invention component signals are derived in separate channels, and means are provided in such separate channels for changing the gain of the channel in accordance with the signal carried thereby to provide for transition between two dir"- ferent modes ot operation, i.e., linear and non-linear.

While the invention may be embodied in an electronic governor, it is by no means limited thereto but may be embodied with equal advantage in speed governors of other types, for example, magnetic or mechanical.

It is accordingly an object of the present invention to provide an improved automatic controller which is capable of extremely rapid response with a yminimum or overswing and without objectionable cycling about the control point. It is a related object to provide a controller in which the iinal control element is correctively moved at high speed, and in which the maximum available power of the corrective means is utilized to eilect the necessary correction. c

It is another object to provide a controller which is capable of controlling systems having a high degree of lag or dead time and which is particularly suited to controlling the speed of a prime mover.

It is a further object to provide an improved automatic controller in which a nonlinear control channel is employed for providing maximum speed of response in the case of large departures but in which the effectiveness of the nonlinear channel is subordinated in the region of the control point.

More specifically, it is an object to provide an automatic controller having novel means for transferring from nonlinear control to linear control upon approaching the control point from either direction.

It is still another object, related to the foregoing, to provide an automatic controller having a number of channels for producing signal components which are added together to form a net control signal and in which the gains of the respective channels are changed in accordance With the magnitude of the signal therein.

It is an object to provide a scheme of automatic control which is extremely flexible in application and which may be embodied in various types of control devices exemplified by the electronic, electromagnetic, and mechanical devices which are described herein. It is a further object to provide a system of control which may be used with systems having a wide range of such operating characteristics as lag, gain, power and speed.

It is, moreover, an object of the invention to provide an automatic control system which not only has an irnproved transient response but which is inherently simple and straightforward, as well as economical, in first cost and in maintenance, using noncritical components and requiring no critical adjustments.

Other objects and advantages of the invention will be apparent upon reading the speciiication and upon reference to the attached drawings, in which:

FIGURE 1 discloses, partially schematically, a nonlinear electronic speed controller constructed in accordance with the present invention.

FIG. 1a is similar to FIG. l, and illustrates the same controller, with the various components rearranged spatially to indicate the presence of linear and non-linear computers formed thereby.

FIG. 2 shows the characteristic of the absquaring element employed in FIG. l.

FIG. 3 shows the variation in servo current as a function of the net control signal.

FIG. 3a shows the variation in servo speed as a function of the net control signal.

FIG. 4 shows schematically a circuit used for increasing gain employed in the system of FIG. 1.

FIG. 5 shows the output characteristic of the circuit of FIG. 4.

FIG. 6 shows schematically a circuit used for decreasing gain employed in the system of FIG. l.

FIG. 7 shows the output characteristic of the circuit of FIG. 6.

FIG. 7a is an enlarged view of one of the break-points in FIG. 7 showing the gradual transition between the two values of gain.

FIGS. 8-l1, inclusive, disclose control systems employing the teachings of FIG. l, but simplified for use in applications where rened control is not essential.

FIG. 12 is a transient speed curve obtained using the nonlinear control system of FIG. 1.

FIG. 13 discloses, partially schematically, a nonlinear electromagnetic speed controller constructed in accordance with the present invention.

FIG. 14 `discloses a magnetic amplifier circuit of the type employed in FIG. 13.

FIGS. 15 and 16 show modified input circuits for use with the magnetic amplifier of FIG. 14.

FIG.V 17 shows the output characteristic of the magnetic amplifier of FIG. 14.

FIG. 18 shows a limiter circuit for use in the control system of FIG. 13.

FIG. 18a shows the variation in servo current as a func- 4 tion of the net control signal when using the limiter of FIG. 18.

FIG. 19 discloses a modified form of the system shown in FIG. 13, including provision for changing gain in the respective channels.

FIG. 2O discloses, partially schematically, a non linear mechanical speed controller constructed in accordance with the present invention.

FIG. 2l is a fragmentary perspective of the gain-changing mechanism employed in FIG. 20.

FIG. 22 is a geometric construction showing the operation of the multipliers used in FIG. 20.

FIG. 23 is a fragmentary perspective showing an alternate mechanism for manually adjusting the multipiers.

FIGS. 24-26, inclusive, show transcient speed characteristic applicable to FIG. 20 for respective conditions of adjustment.

ELECTRONIC NONLINEAR GOVERNOR Referring now to the drawings, FIGURE l shows schematically one form of the present invention. The arrangement shown in this figure is intended for use with controlled devices, for example, internal combustion engines, which exhibit substantial lags and dead time, and in particular systems in which the summation of the lags and dead time is approximately 1/s second or more. In the sections which follow, the invention is embodied in somewhat simpler system for use where the number of large lags and dead times is not excessive, or where precise control is not essential, or where low amplitude cycling about the control point may be tolerated.

The automatic controller of FIGURE 1 is used for governing engine speed, the engine being indicated diagrammatically at 30. The engine speed is controlled byl a throttle 3l and means are provided for continuously measuring the engine speed. In the present instance this measuring device includes a tachometer generator 32 and a source of auxiliary voltage 33 which is settable by a control 34. The circuit is so arranged that the output voltage of the tachometer generator is in series with voltage source 33, With the polarities in bucking relation, so that the net voltage appearing at output terminal 35 has direction and magnitude which correspond to the direction and magnitude of the departure in speed. The tachometer may be of the D.C. or A.-C. type; in the latter event the output is rectified by a rectifier 36 as shown.

Where straight isochronous control is desired, the rectified tachometer voltage is simply bucked against the' adjustable Voltage from the source 3?, the circuit being completed by interconnecting terminals 37-38. How4 ever, where it is desired to provide droop, as for example, Where a number of engines are operated in parailel with one another, a source of droop voltage 40 is provided having a control 41 which is directly coupled to the throttle of the engine by means of a mechanical link 42. Such voltage is added in series by transferring the connection from terminals 37-38 to SL39.

The net voltage at the terminal 35 forms the basic deviation signal which, as an initial step, is passed through a filter 50. This filter is `so constructed as to remove the electrical noise which accompanies the signal. The term noise is a general one and refers to any extraneous high frequency components in the control signal. In an engine, noise results primarily from the fact ythat power is obtained from separate explosions and from impact of the individual gear teeth where gears are used. The lter includes an RC network 5l and an operational amplier 52 having associated resistors 53, 54 and feeding an output terminal S5.

During the course of discussion frequent reference will be made to operational amplifiers, indicated in each case by the conventional triangular symbol. It will be under`- stood that such ampliiiers are standar-:lunits of the typef used in analog computing apparatus, such, for example,I as described at page 152 in Electronic AnalogComputers,f

alessia .by Korn and Korn, McGraw-Hill, 1952, and which are commercially manufactured by George A. Philbrick Researches, Inc., of Boston, Massachusetts. Reference is made to the descriptive literature covering the Model K2`-W amplifier for operating characteristics. A high value of feedback insures linearity; `for practical purposes the gain of a given stage in the ratio of the amplifier shunt or feedback impedance to the series or input impedance and is independent of minor Variations in tube characteristics.

The output of the amplifier unit 52 is applied to two lines 57, 58. In the first, the deviation signal is utilized directly; in the second it is differentiated for forming derivatives. From the line 57 the signal passes through a gain changer 59 which Wil be described in a subsequent section. The output terminal of the gain changer is connected to the first input terminal of a signal adder 70 having input terminals 71-74 and an output terminal 75. The purposer ofthe signal adder is to add together the error signal and its derived components to form a net control signal at theoutput terminal 75. This net signal is then used to control a,motor operator indicatedgenerallyrat 76, which includes a final control element 77 connected to the throttle 31. The motor operator will be discussed at a later point.y

Referring back to the line 58 at the output of the filter 50, a first difierentiator unit Sii is provided having a .differentiating capacitor r81, an input resistor 82, an amplifier 83 and a feed-back resistor 84. The differentiator unit acts to ydifferentiate the input signal, i.e., to take the first derivative With respect to time. The output or derivative signal is applied to an output terminal lS and is fed to two linesy 36, 87. The first line 86 carries the directly utilized signal which is fed to the terminal 72 of the signal adder 70 via an inverter 90 and a gain changer 96. The inverter is simply an amplifier unit having a gain of unity used to restore propersign and includes an input resistor 91, any operational amplifier 92 and a feedback resistor 9,3. The signal arriving at the terminal 72, because of the differentiation which has occurred in the unit Si), is proportionate to the first derivative of the speed deviation.

In order to obtain a second derivative signal, a second diiferentiator unit 100 is used having a differentiating capacitor 101, an input resistor 102, an amplifier 103 and feed-back resistor 104. The second derivative signal, appearing at output terminal 165, is fed to two lines 106, 107. Because of the reversal of sign. occurring in the difierentiator, it is necessary to use' an inverter 110 in the line 106, the inverter having an input resistor 111, an amplifier 112 and a feed-back resistor 113. The output terminal 114 of the inverter is connected to the third input terminal 73I of the signal adder 71) via aline 115 and a gain changer 116v as shown.

In accordance with the present invention, novel means are provided for producing a control signal which not only includes the error signal and derivatives thereof but which also includes an auxiliary control signal which is an absquare function of the sum of the first and higher order derivative signals. The term absquare is a coined term. It is thesame as the square function in magnitude but differs from the square function in the respect that it preserves the sign of the quantity acted upon. Thus, if the quantity acted upon were, say, minus 2, the absquare of the quantity would be minus 4. If the quantity acted upon were a plus 2, the absquare would be plus 4. In considering the formation of the absquare signal, attention will first be directed. toward' means for producing the `derivative signal vwhich is acted upon by the absquaring error signal.

In they presen-t instance the components of the derivative signal used for absquaring are added togetherby a derivative adder 120 having input terminals y121, 122, 123, and an output terminal 124. As to the first derivative, this is supplied from the difierentiator 8) via the line 87. The second derivative signal is obtained from the output of the second diferentiator 100, and is supplied to the derivative adder by the line 107. To obtain a third derivative signal, the output of the inverter 4110 is fed via a line to a third diierentiator unit 130 having a differentiating capacitor 131, an input resistor 132, an amplifier 133 and feed-back resistor 134. The output terminal 135 of the third differentiator unit is connected to the input terminal 123 of the derivative adder.

In the derivative adder 121i a resistor network is provided consisting of resistors 141, 142, and 143. These resistors have a common output terminal 144 feeding into an amplifier 145 having a feed-back resistor 146. Thus, the derivative signal which exists at the output terminal 124 of the derivative adder is proportional to the sum of the rst yto third derivative signals with their respective constants.

In carrying out the present invention, the derivative signal is fed into an absquaring rdevice 148, which forms a part of the signal adder 71.1. The signal adder 70 may thus be more properly referred to as an adder-absquarer. In accordance with one of the features of the invention, ythe absquaring device 1148 is in the form of a nonlinear resistor element in which the current varies as the square of the applied voltage. The theoretical absquare curve is set forth at 149 in FIG. 2.

The selection of a resistor material having the desired absquaring characteristic is a problem which is well within the scope of one skilled in this art. A number of noulinear resistor materials are available on the market which exhibit the desired characteristic in varying degrees. The material known as thyrite has been found -to be particularly suitable, the characteristic of thyrite (Type V-3,900, 353 sold by the yGeneral Electric Company) being set forth at 15? in FIG. 2. It will be understood, however, that the invention is not limited to the use of this material but would include the use of any other materials 0r devices exhibiting the same general input-output characteristic.

The output signal of the absquaring device 143 is added to voltages derived from the resistors 151-153 which carry the deviationsignal and first and second derivative signals respectively. Such resistors are preferably variable to enable the signal components to be varied with respect to one another. The net signal is fed into an amplifier 154 having ya feed-back resistor 155 to produce a net output signal at the terminal 75 which will be referred to in subsequent analysis as -c2, where 2 is a control function and c the gain constant of the circuit.

Attention may next be given to the motor operator 76 which converts the signal from the control unit into mechanical movement of the throttle. The first part of kthe motor operator is a cathode follower stage 1513 having vacuum tubes 161, 1&2, and supplied by a regulated D.-C. power supply 163. In order to produce on output signal which is proportional to the signal at the terminal 75 in direction as well as magnitude, the signal fed to the tube 162 is inverted in phase by an inverter 17d having an input resistor 171, an amplifier 172 and a feed-back resistor 173. The inverter has a gain of one, yhence the signal at the output terminal 164 of the inverter is simply -l-CE. In operation one tube conducts more and the other less, depending upon the polarity of the voltage, causing corresponding voltage increase and drops in the cathode resistors 174, 175. i'

Connected across the catliodes of tubes 161, 162 is a control winding 176 of an hydraulic servo device177. The servo 'has a pilot valve 178 which cooperates with a supply port 179 and a sump 180, to control the flow of fluid to a servo cylinder having a piston 181. The piston l181 is connected to the final control element 77, which in turn operates the engine throttle.

Return movement of the throttle is obtained by providing a return spring 182. The pilot valve in the present device is provided with entering springs 183, 184 as well as stops ESS, Li, which prevent the pilot valvefrom moving substantially beyond its full on or full oit condition. Hammering of the stops, is, however, minimized by limiting the current which is supplied to the winding 176, the current versus control signal characteristic being set forth in FIG. 3. It will be noted in this figure that limiting occurs below the value of current required for the pilot valve to strike its stops. Such limiting is accomplished by utilizing the effect of current saturation in the tubes lei, 162. The point of saturation depends upon the tube characteristics, circuit resistances and operating voltages, and is a matter which is well within the capability of one skilled in the art.

ln practicing the present invention, it is desirable to employ a servo in which the speed of response of the output under fullon, full on conditions is as high as possible. In a practical case7 the speed of the servo piston is limited by the allowable size of the servo device and the pressure and rate of flow of the duid which is available to operate it. In general, it is not desirable for the Servo device to consume more than a traction of a percent of the maximum power of the engine which it controls. As a practical matter, when controlling an average internal combustion engine, I prefer to use a servo having a maximum speed on the order of to l0 or more inches per second, when subjected to normal frictional loading.

The servo device and its associated cathode follower stage include a number of design parameters which must be taken into consideration in working out a practical design. It will suflice to say that the overall characteristic of the motor operator 76 should follow the curve set forth in FIG. 3a of the drawings. Here it will be noted that the servo speed varies directly in proportion to the applied control signal c2 up to the point at which the maximum servo speed is attained. In carrying out the invention, I prefer that the motor operator be so designed that the maximum servo speed is attained with a control signal c2, which is only about IAO of the maximum control signal, the maximum control signal being defined as that which results upon making an extreme and abrupt change in the loading of the engine 30, for example by dropping full load. This insures that the servo will operate at its maximum speed of response in the face of al most all normally encountered disturbances, and excepting only those minor disturbances which occur in the vicinity of the control point under conditions of substantial equilibrium. In summary, it will be seen from FIGS. 3 and 3a that the motor operator or power means is linearly responsive to the net control signal c2 but saturates (i.e., does not increase its response) when that control signal exceeds a predetermined value. On the other hand, the net control signal c2 is continuously variable over a given range which substantially exceeds predetermined band of values to which the motor operator linearly responds. Thus, the motor operator will operate full on or full oit during the correction period which follows a severe disturbance of equilibrium.

One skilled in the art might Vconclude from the foregoing that the operation of the control system as a whole would be extremely erratic, comparing such system with conventional linear systems in which the servo speed varies in accordance with the magnitude of the disturbance over almost the entire operating range and in which maximum servo speed is attained only under the most extreme conditions. It is found, however, that the absquaring function and the manner in which itis utilized in the present circuit produce a control function which is eminently suited to the high speed servo action, producing a transient response characteristic which is morerfavorable than that attained in highly developed control systems of more conventional types.

Procedure for Adjusting Electronic Nonlinear Governor The arrangement described above and shown in FIG. 1

' includes means for adjusting the various components of Controls Magnitude of- Resistor In- Filter 50 Signal fed into controller as a whole. Signal Adder 7 Deviation signal.

0 First diierentiator Unit Signal Adder 70 Second diterentiator Unit All derivative signals. First derivative signal. All second and higher deriv- 'lllid ditierentiator Unit Derivative adder ahsquarer. Third derivative signal for absquarer.

`required to make one-half a revolution.

vIn carrying out the present invention, the circuit shown in FIG. 1 is utilized for obtaining a control signal -c2, at output terminal 75, where c2 has the following form:

Here E is a control function; x is the speed deviation; x', x and x" are rst, second, and third derivatives of x; and al, a2, `b and c are constant coefficients. I have devise'd a novel procedure for adjusting the various resistors in terms of the coefficients a1, a2, b and c. In this connection it can be shown that the above coefficients may be given physical significance in terms of the system which it is desired to control, as follows:

a1=the sum of the time lags (including dead time), normally measured as time constants.

a2=the sum of the products of the time lags taken two at a time.

b=the inverse of` the product vof twice the gain of the system and the maximum servo speed.

czoverall gain coeiicient.

The only one of the above coeicients which cannot be immediately ascertained by tests on the system to be controlled is c; a1, a2 and b being stated simply in terms of time lags, the gain of the system, and maximum servo speed. Attention may iirst be given to the procedure for determining the time lags in a practical case, for example, a gasoline engine, where three primary lags are usually present. The iirst is the throttle lag, that is to say, the time interval which occurs between making a step change in the throttle setting and the time that the new value of torque is applied. Since the new value of torque will be approached along an approximately exponential curve, the time lag can be considered to be the interval required for the torque to reach (l-l`c) of the new value, where c is the base of natural logarithms.

Another lag in a gasoline engine is the interval between the time that a given change in torque results in a new value of speed, the delay being due to various factors, notably Ythe inertia of the engine andk connected load. Here again, as a close approximation, the time lag can be taken to be the time required for the speed to reach l-lc) of the new value. A third factor is the dead time due to the intermittent character of the explosions. Ex-

erience has shown that this dead time in a typical fourcycle engine is the period required to make one revolution and in the case of al two-cycle engine is theperiod The iirst two lags are characteristic of the engine and do not vary substantially with speed. For maximum accuracy, however, all three lags should be determined at the design speed at particular application.

Having this ascertainedv a1 and a2, ldetermination of b requires knowledge of system gain, which is defined as the initial value of the first derivative of the controlled variable (here, speed) provided by the displacement of the final control element (the throttle) when the step change is made in the final control element from equilibrium. The maximum servo speed is defined as the greatest speed of which the final control element is capable. In the present instance it may be measured by observing the speed of the element 77 with the pivot valve 177 open all of the way.

I have found that c may be determined in a particular instance by a procedure which has as its rst step adjusting the device for linear control with the absquaring channel made ineffective. By linear control is meant operation using a control function having only those terms which are characteristic of a linear differential equation. The procedure used in such preliminary adjustment is covered in the following section.

Preliminary Adjustment for Linear Control In order to operate the system under linear control, the control system is set up as shown in FIG. l with the absquaring channel (line 147) open-circuited and with the gain changers 59, 96, 116 omitted. Thus the only signal components which are fed into the adder 70 are proportional to the deviation x, its first derivative x and its second derivative x". The control function 2 for linear control is given by the following:

where C, A1 and A2 are constant coefficients which must be determined. Since the expression is linear, the determination of coefficients capable of yielding stable operation is well within the skill of the art. Procedures which may be used are set forth in various texts on automatic control. For example, Thaler and Brown in Servomechanism Analysis, McGraw-Hill, 1953 (p. 6 et seq.) describe a procedure which makes use of the following transfer functions for an automatic controller:

IQF S =K1 +A1+AZS 3) where K1 is a constant, s is an operator, F(s) is a function of s and A1 and A2 are the constants set forth above. Let K2C(s) denote the known transfer function of the systern to be controlled, where K2 is a constant and C (s) is another function of s. As described by Thaler & Brown at pages 127-136, the total transfer function of the control loop, when the loop is broken, is therefore Assumed values are applied to C, A1 and A2, and roots are determined for the following equation:

The roots should have large negative real parts for stability. A simple method for obtaining these roots is found in my article in the American Mathematical Monthly, June-July, 1948 (pp. 335-342). If the polynomial is of a Very high degree and difficult to solve, the test for stability used by Routh may be applied as covered in the Thaler and Brown text, p. 151. By way of example, both A1 and A2 are usually less than unity and A2 is usually less than A1. Thus as a start, values of l/5 and 1/25 may be assigned to A1 and A2 and may be varied until the Routh test shows stability. If necessary, slightly different values of A1 and A2 should be tried until stability is indicated. If desired, the recently `developed frequency response technique may be used to determine values of A1, A2 and K1 as described by Thaler and Brown at pp. 126, 13S-147. After the coefficient K1 is determined, it is a simple matter to determine the constant C from the expression C=K1/k9 where k2 is the constant of the motor operator. v

The above ,procedure yields the coefficients for linear control. The next step is to adjust the settings of the variable resistors in the controller to correspondv to the values of such coefficients, in accordance with the following procedure.

It will be understood, first of all, that the tachorneter generator produces a voltage which is proportional to speed. This is bucked against an auxiliary voltage to produce a net deviation voltage x. The magnitude of the auxiliary voltage is set by the control 34 so that x=0 at a particular speed, such speed being defined as the control point. Any departure of speed from the control point causes a corresponding departure in the deviation voltage.

In order to get rid of the noise in the signal, it is passed through the filter 50. The filter is preferably adjusted to have as short a time constant as possible consistent with adequate filtering and which in the case of an internal combustion engine is about 1/100 sec. n

At the output of the filter 50 the filtered' signal voltage is k1x where The signal voltage undergoes further transformation upon passing through the adder 70, being multiplied inthe ratio R155/R151. The overall change in x therefore from the input terminal 35 yto the output terminal 75l and which by definition is the coeicient C, is given hy the .expression R155 may be assigned a convenient value of 1(1)(i ohms. It is also convenient to make R51=R53 and it will therefore be assumed throughout that k1=2, keeping in mind, however, that the gain of the entire loopl may bechanged by adjusting these two resistors in some other ratio. SIlQe coefficient C is known by calculation, the above expression gives the proper setting for R151 in the deviation channel.

Next, the rst derivative signa1-CA1x is formed using the differentiator and inverter p90, the differentiator beingy Supplied with a signal 2x from the filter 50. It is desirable t0 Provide additional filtering in this Channel, hence `the resistor 8,2 is provided, forming an RC filter with the differentiating capacitor 31. The value of ,the capacitor may be conveniently taken as 106 ,-farads, The filter R82C21 may have a time constant of about 1/,100 second. Thus Rs2 is fixed at 104 ohms. In order to avoid any attenuation of the coefficient while differentiating, the resistor 84 is chosen so that Rs4Ca1=1 (8) vSince C111 is 10*6 farads, then R184 must be 106 ohms. Because of the inversion which takes place in lthe differentiator, the output voltage is -2x and an inverter 90 .is used to restore proper sign. In the inverter 90, the resistors 91, 93 are made equal to avoid any attenuation, although it shouldI be kept in mind that the derivative rsignal may be attenuated here if desired simply by adjusting the ratio of Kga/R91. Using equal values for resistors 93 and 91 results in a voltage of 2x at the terminal 94 for feeding intothe signal adder.

The signal to be obtained at ythe output of the adder 70 is .CA1x'. The derivative signal undergoes a change when passing through the ,signal adder 70 which is expressed by the ratio R15/R152` Thus The resistance R155 was previously set at 106 ohms.

The values of A1 and C were previously calculated so that R152 may be obtained from (9) above.

Next, .attention is given to the second derivative signal which is rproduced by the second differentiator and inverter 110. The differentiator is supplied with a ysignal 2x from point 9.4 inthe first derivative channel. The procedure for obtaining the resistor settings for the second derivative signal is completely analogous to that set forth above. Additional filtering is provided by the resistor 102 in combination with the differentiating capacitor 101. As before, the capacitor 101 is chosen at a convenient value, any -6 farad, R102 is chosen to provide a time constant of l/ 100 second or less, and R104 is chosen so that the signal coefficient is not attenuated. This produces an output voltage -2x. The latter is inverted in the inverter 110 with R113 set equal to R111 so that the output voltage of the inverter is 2x".

The desired second derivative output signal from the adder 70 is CAzx. The expression relating to input and output is The only unknown in this expression is R153 which may be numerically determined. This completes the preliminary yadjustment of the control device for linear control and the system may now be turned on and should operate stably. Small trimming adjustments may be made in the settings of the resistors 151, 152 and 153 to vary the amount of each of the components to improve the control in response to disturbances such as changes in loading. The filters may also be adjusted to minimize servo jiggle While keeping the filter time constants as short as possible.

Adjustment of Nonlinear Channel Attention is next given the channel which feeds the absquaring resistor 148. This channel includes a third diiferentiator 130 for taking a third derivative, using as input the second derivative signal from the inverter 110. Further filtering is provided by the resistor 132. As a first step, the capacitor 131 is assigned a convenient value of 10-6 farad and the associated resistors 132, 134 are chosen to provide a time constant of 1/ 100 second and unity gain respectively as in the case of differentiators 80 and 100. The output of the third ditferentiator is therefore -2x'. This signal is fed into the derivative adder 120 where it is attenuated in the ratio RMS/R143. Since the sign is also reversed, the third derivative component at the ouput of the derivative adder is 2(R146/R143)x". For convenience, resisto-r '146 may be assigned a value of 106 ohms. The resistance R143 is however unknown, and, to determine the proper setting for the resistor, the system is put into operation on linear control with the highest or third order derivative absquaring term added.

Accordingly, the input terminals 121, 122 of the derivative adder are open-circulated and the system is started. Starting with a high value for R143, the resistance is gradually cut down until the jiggle of the pilot valve in the motor operator is the maximum which can be tolerated for the particular application. The nal value of R143 is then noted and the system may be shut down.

Referring to FIG. l, the signal fed into the absquaring The quantity a1 is known, being defined as the sum of the lags, thus giving the value of R142. Similarly, in the case of R141 which is fed by a signal -2x, we know that 2x'-R146=k7fc enabling R141 to be ascertained.

l2 Hence at the output of the derivative adder 120 the total signal is given by Cu from After passing through the adder, the nonlinear signal becomes @il 2 l RE /l R 141 In] Rm absquare [zu -l-Rmx -l-Rmx (17) Comparison with expression (l) above shows that All of the factors in this expression are known except the gain coefficient c, which can be determined numerically.

Knowing c, it is possible to readjust resistors 151, 152 and 153 to give the proper coeilicients in the linear channels, namely, cx, ca1x and cagx required for full nonlinear `operation. The voltage at the input side 71 of resistance 151 is 2x which is multiplied by when going through the adder. Thus R151 from which R151 may be numerically obtained. Similarly, the first derivative voltage at the input 72 of the adder is 2x', therefore,

from which R152 may be obtained. Also the second derivative voltage at the input 73 of the adder 7i) is 2x, thus which determines R153. This completes the setting of all the resistors to provide a total nonlinear signal of -ce at the output terminal '75 of the adder 7 (l.

Use of Gcn'n Changers An automatic control system constructed as shown in FIG. l `and adjusted `as outlined above will produce satisfactory control in systems Where the signal components corresponding to the high order derivatives, say those higher than the third, are so low as to be negligible. Satisfactory -operation is believed to be due in some measure to the particular shape of the nonlinear resistor characteristic for low signal values. Although it is by no means obvious from the characteristic shown in FIG. 2, I have observed that commercially available nonlinear resistors, for example,'thyrite, depart from a true parabolic shape and become linear in the region of the origin. This tends to reduce any tendency toward cycling about the control point.

It is found in practice that the nonlinear signal obtained as above when fed into a high speed motor operator results in movement of the final control yelement at substantially top speed even in response to relatively small lspeed disturbances. The .present system is characterized by anL Aaverage vservo speed which is many times greater than conventional linear control systems where full speed of the final control element occurs only during the most extreme departures ofy the condition from the rcontrol point. While such rapid response brings about a number of advantages, it is found that with some .controlled systems, there is a tendency toward abrupt onoff action in they region of the control point which is evidenced as low amplitude cycling.

While low amplitude cycling is lnot per kse objectionable, I have yfound that operation under conditions appreaching equilibrium may be improved by reducing the relative eifectiveness of the absquare signal in the region ofthe control point. r This is accomplished in the present v instance by inter-posing gain changers in one or more of the linear channels to change the gain to a more favorable value-when the magnitude of the signal in the respective channel is less than a predetermined low value. More specically, I provide gain changers in the deviation channel, as well as in the rst and second derivative channels, soadjusted that when the respective Signals are small, as they will normally be withthe system in the ,region of the control point, the grain of the channel isA ychanged to correspond to that gain which would be employed for straight linear control. This will be made clear by reviewing the adjustment procedureoutlined in the preceding section. It will be recalled that during the adjustment procedure the system was, as a preliminary step, adjusted kfor stable operation at the control point with the absquaringch-annel disconnected; Such preliminary adjustment involved determination of coeiicients C, CAl and CA2 and corresponding adjustmen-t of the gain in each channel to give such control coefficient-s. This was accomplished by adjusting the channel resistors,` Subsequently, with the full control circuit, including the absquaring channel, in operation, the circuit resistances were adjusted to provide a diierent set of control coefficients, namely, c, cal 'and Ca2.

In carrying out the present invention the gain changers, indicated in FIGA l at S9, 96 and 116 (in FIG. 1 and throughoutv the drawings, the blocks representing gain changers are labelled with the letters GC), are connected in the x, x and x channels to perform the following respeotive functions:

(l) Gain changer 59 changes the coeflicient of x from c to C whenever the absolute value of the x component is` less than a predetermined amount x1.

(2) Gain changer 96 changes the coefficient of x from ce1 to CAU whenever the absolute value of the x component is less than la predetermined amount x1.

(3) Gain changer 116,. changes the coefficient of' x" from Ca2 to CA2 Whenever the absolute Vahle of the x con-iponent is lessjthan a predetermined amount x1".

The points x, x' and x" at which. the change in gain Itakes yplace may be referred to as break points. In

general, since transfer occurs for both positive and negative values of signal, theydefine narrow bands of low signal operation. I have found that it is desirable to individually narrow down these bands as much as possible. The procedure tor setting the band Width is covered in the subsequent sectiony on adjustment'. Y

The change in gain, i.e., coefcient, at the break point,

i may be up or down depending upon Whether the desired low signal coetlicientV is greater or less, than the high signal coefficient. In the device under discussiomlthe gain in the deviation channel is decreased under low signal conditions while the gain in the iirst and second derivative channels is increased. In the present ydevice the circuit used` for reducing the gain differs from that employed for increasing the gain. Where an increase in gain is desired under low signal conditions, I prefer to use the circuit arrangement shown at 199 in FIG. 4. Such circuit includes an operational amplifier 200 having an input resistor 2M and a shunt resistor 202. Means are provided for changing the value of the effective shunt resistance in order to change the gain. In the present instance the value of the shunt resistance is reduced by shorting across resistor 202 a double diode 203, 204 having a series resistor 205 and which conducts when the input signal is greater than the break point but which is nonconduetive and therefore ineffective when the input signal is less than the break point. The first diode 203 is supplied by a voltage divider consisting of resistors 206, 207. The voltage divider is above ground potential so that the first diode is effective for positive input signals. The vsecond diode is connected to a second voltage divider consisting of resistors 208, 209, which is below ground potential, with ythe result that the diode 204 is effective for negative input signals. The polarity of the input signal is restored by an inverter 210 of unity gain. The resistances R207 and R208 are taken small compared t0 R202 and R205. y

The operation of the circuit and the adjustment of the various resistors'will be made clear upon reference to FIG. 5,which shows the desired output characteristic. yFor koperation beyond the break point, the gain changer should have a gain m of unity, as indicated. For signal values of less than the break point the gain changer should have a gain of n which, in FIG. 4, is larger than m. The ylow signal bandwidth is indicated at w. For the three gain changers, 59, 96 and 116, n is defined by the during nonconduction. The above two expressions inrlow-signal range.

r`resistors 222, 223, which conducts whenever the input voltage is beyond the obtained for R202 and R205. This completes the gain adjustment but does not determine the break point. The break point is adjusted by varying the resistors 207, 208 to whichefunction reference will be made. The magnitudes of the voltage supplied lto the diodes,`because of symmetry, are the same and resistors 207, 208 may be conveniently ganged together.

The above discussion covers a gain changer for use where an increase in fcoeiiicient is desired within the Where a decrease of coeicient in such yrange is desired, I prefer to use the ,arrangement shown at 119a in FIG. 6, and whose characteristic in set forth in FIG. 7. In the circuit of FIG. 6 an opera-tional amplifier 2,20 is used having a shunt resistor 221 and series A double diode 224, 225 is used diodes are nonconductive the series resistor 22S-is in the n circuit and the gain has a lower value n, n being deined y as setforth above. The polarity of the input signal is restored by an inverter 230. i Since m by definition is unity, and assuming the resist- 'j' ance of the conducting diodes to be negligible,

i It will be seen from FIG.

during nonconduction, and

R221= nR222 during conduction.

The above two equations have three unknowns, and the resistor 221 may be therefore assigned a convenient value of l05 ohms. This permits practical numerical values to be obtained for resistors 222, 223.

The above covers the adjustment of the two values of gain, but does not cover the setting of the threshold points. This is accomplished by simultaneously varying the resistors 207, 208 (in FIG. 4) and 227, 22S (in FIG. 6) which are respectively ganged together. It is to be noted that the arrangement shown in FIGS. 4 and 6 enable the band width to be adjusted entirely independently of m and n, the two values of gain. As an initial approximation the low signal bands may be adjusted for a Width which is on the order of 10% of the maximum values of each of the respective variables. A more refined adjustment requires the system to be set in operation and a trimming adjustment to be made. With the system operating, the ganged resistors which control the band width are reduced progressively in each of ythe gain changers S9, 96 and 116. The gain changers should be adjusted `in rotation, making the resistance in each case as low as possible without causing erratic operation or cycling about the control point when small disturbances are introduced into the system. A minimum band width in each channel insures that Ithe coefiicients corresponding to design nonlinear control are eiiective, as close as possible to the control point. It will be found yin a governor of the type described that the width of the low signal band in the x channel will be approximately 2% of the maximum voltage in that channel, while the width of the bands in the derivative channels will be approximately 10% of the maximum voltage in each of these channels. In the event it is possible to reduce the controlling resistance to zero in any of the channels, it will be apparent that the gain v changer in such channel is not needed and may be taken out of the circuit.

It is one of the features of the gain-changing arrangement described above that transfer of the entire net control signal from the nonlinear to the linear condition, upon approaching the control point, is entirely avoided. Any transfer between the two conditions of gain, on the contrary, occurs on an individual basis in the respective channels carrying the x, x', or x" signals and the criterion for change of gain is the signal level in the particular channel. Such individual transfers can, and normally will, take place at diiferent times in the respective channels. The overall transfer from nonlinear to linear operation when the control point is approached therefore ltd trolled element, whose speed is the variable condition controlled by the motor operator` 160, 177, 181 acting on the throttle 31. The status or speed of the controlled element is sensed by the tachometer 32 which through the rectifier 36 produces a voltage representative of actual engine speed. The manually adjustable wiper of potentiometer 34 is a controlling element, and the position or status of the latter (i.e., desired reference speed) is indicated by the voltage thereon. These two voltages are bucked to produce a deviation or error signal equal to the difference in status. This error signal is supplied through the iilter and ampliiier to the input 55 of a linear computer indicated by the dottedvline enclosure. By virtue of the connection 57, the ditferentiator 80 andthe differ entiator 100, previously described, the output of this linear computer is constituted by signals proportional to the error, the first derivative of the error, and the second derivative of the error appearing on lines 57, 9S and 115. Since all of these signal components are linear, the dotted kline portion is a computer which produces as its output a linear integro-differential function of the error.

The output of the linear computer forms the input to a non-linear computer comprised of resistors 71-73 and the thyrite resistor 148. 4The latter receives the out put of summing ampliiier 146 whose inputs are received from lines 87, 107 and differentiator 130. Thus, the output of the non-linear computer is the input to the summing amplier which produces on terminal 75 the net trol signal is supplied to the power system and actuates the latter so that it is turned full on or full ofi to cortakes place in steps and there is no need for the system as a whole to decide whether to be linear or whether to operate according to the full nonlinear control function. This not only results in smoother control, avoiding tentative or indecisive action, but makes all circuit adjustments much less critical.

Nor is there any abrupt switching at the break point. In the circuits described vacuum diodes have been used in which there is no sharp break point and in which conduction increases more or less gradually over a range of plate voltage. This causes a rounding of the break point on the characteristic curves and a gradual change of gain from m to n, the control easingv from one condition to j the other. Such transition, obtained in accordance with connections to FIG. l, but differs only in that the system lla that the engine 30 isa con`v rectively adjust the throttle and engine speed, except for linear operation when the error derivatives are small, as previously described.

It will be readily apparent to those skilled in the art that the principal components of the serially connected linear and non-linear computers are lpassive components which are small, reliable and readily available. That is, the thyrite resistor 143 for producing a non-linear absquare signal is passive, as are the capacitors 81, 101, 131 which are the principal parts of the ditierentiators 80, 100,

' 130. The two computers illustrated in FIG. 1a may be constructed entirely of passive elements and the operational ampliiers 83, 103,134, 145 omitted. In that case, amplifiers located either at the input of the linear cornputer or the output of the non-linear computer may be used toincrease the iinal control signal to the desired level.

Electronic Governor- Second Embodl'ment any means for generating a third derivative signal. In the systems shown in the subsequent FIGS. 9, 10 and l1, still further simplification has been brought about. While the adjustment of the circuits shown in FIGS. 8-11, inclusive, will be largely apparent in view of the discussion of the adjustmentof FIG. 1 above, nevertheless the adjustment procedure applicable to 'each will be reviewed briefly for the sake of completeness of disclosure.

` Referring to FIG. 8, the circuit components shown correspond to those in FIG. l Iand corresponding reference numerals are employed. The portion of the circuit to the right of terminals 75, 164 will be understoodto be the same as in FIG. l. In utilizing the circuit `ot FIG. 8,

'I vemploythe fol-lowing formof'control characteristic:

As a ypreliminary step, the circuit is first adjusted to provide stable operation using linear control, and in accordance with the following control function:

C2=Cx-l-CA1x'-ICA2x This requires knowledge of the linear coeiieients C, A1 and A2, which are determined using known procedures already discussed. For linear control the absquaring channelis disconnected, for example, by opening the circuit at terminal 74 of the adder '76. The gain changers 59, 96 and 116 are 4omitted during this portion of the adjustment, The7 complete `linear ;signal,-.C21at the output, may be expressed in terms of the circuit parameters, as follows:

Rsi-P1553) 93)p R155) n R13 R84O81 R91 A104010! R111 R153 x 2R155 217-2155 21E155 C' l 2' R111?+ R111` R113qd `Byrequating coeiicients in (27) and (29) above, it is seen that Since R155 is l0s ohms, the only unknowns are R151, R152 and R153, which may be numerically obtained and the resistors set accordingly. The system may then be started and should operate stably.

With the system operating under linear control, trimming 'adjustments are made in the settings of resistors R151-R153, if necessary. rhe absquaring channelpreviously disconnected is now connected so as to inject a gradually increasing amount of second derivative absquaring signal. Toy do this, trimmer Ml is disconnected and resistor 142 is gradually decreased from a high value up tothe point ,which produces maximum tolerable jiggle in the output or Ithrottle servo. This circuit adjustment enables the gain coefficient c inA expression (26) to be determined, the other coefficients a1, a2 and b being known. This is done as follows:

The nonlinear control function (26) is set forth in terms of the circuit parameters which aiect it, thus Jl ln the above expression, ka is determined experimentally, being the ratio c0/c12, where c1 is the sinusoidal input Voltage to the absquaring resistor andeo the resulting output voltage at terminal 75, using .the same test setup as described in connection with FIG. l. 1

Taking advantage of the same simplifications as were made in the linear expression, (33) becomes 215155 213155 2R155 '32 R111x+ R115L l R111+ 2R14G 2R14!) il 1, 1 1 x/ y a sq lare Rm Rmx on This may be rewritten 2R155 V22'5155 i 2RM c :c

Z R151 H R111 L R111 x cn4 Rm absquare [Mel-'15-1 xf] (35) Rm R112 1 1 Equating coeiicients in expressions (35) and (26) gives the following:

R141 Y G1 R142 from which R141 may be determined,

R 4s 2 b=4a -L s? c R111 c 1 from which, knowing R111, c may be determined,

'212115 c 38 3,151Y from which, knowing c, the setting of resistor 151 may be determined,

2R 155 ca 39 n* 1 Rm from which the setting of resistor 152 may be determined, and v,

' 2113155 a 40 c 2 :R153 from which the setting of'resistor 153 may be determined. yThisfcompletes the determination of settings for design non-,linear control in FIG. 8. After reconnecting the terminal 121, the system should operate stably, subject to minor .trimming adjustments. Gainchangers 59, 96 and 116 may be added to thecircuit, if desired, in accordance with the procedure described in connection with where C andA are known, as above.` For linear control, the absquaring channel is disconnected by backing oil` resistor 142 all the way and by opening the circuit at 121. Stated in terms of the circuit parameters, (42) becomes R51+R53 R155 Oz( R53 R151 arl RliRss) R93)y R53 2584081 R-Ql R151 27 (43) For simplicity, the following resistors may be made l()s Ohms; R531 R541 R84, R91, R931 R104, R146, 21nd R155- A150 

24. IN A SERVO CONTROL SYSTEM FOR REDUCING A DIFFERENCE IN STATUS BETWEEN A CONTROLLED ELEMENT AND A CONTROLLING ELEMENT, SAID SYSTEM INCLUDING SENSING MEANS PRODUCING SIGNALS RESPECTIVELY REPRESENTATIVE OF THE STATUS OF SAID CONTROLLED AND CONTROLLING ELEMENTS, THE COMBINATION OF; ERROR-SIGNAL MEANS CONNECTED TO SAID SENSING MEANS PRODUCING AN ERROR SIGNAL SUBSTANTIALLY EQUAL TO SAID DIFFERENCE IN STATUS; COMPUTER MEANS PRODUCING AN OUTPUT WHICH IS A CONTINUOUS NON-LINEAR DIFFERENTIAL FUNCTION OF ITS INPUT; MEANS FOR SUPPLYING SAID ERROR SIGNAL AS THE INPUT TO SAID COMPUTER MEANS; A POWER SYSTEM PRODUCING AN OUTPUT THAT IS CONTINUOUSLY VARIABLE IN MAGNITUDE BETWEEN TWO PREDETERMINED LIMITS; MEANS CONNECTING THE OUTPUT OF SAID COMPUTER MEANS TO SAID POWER SYSTEM FOR CONTROLLING SAID POWER SYSTEM SO THAT SAID OUTPUT OF SAID POWER SYSTEM CAN BE VARIED FROM ONE OF SAID LIMITS 